matroid 上的顺序线性契约
Sequential Linear Contracts on Matroids
AI总结：
本文研究了在 matroid 约束下，通过线性契约激励代理依次采取行动以最大化主人效用的问题。
摘要：
在本工作中，我们研究了在 matroid 约束下进行的顺序契约。在顺序设置中，一个代理可以依次采取行动。在每次行动后，代理会观察到该行动的随机价值，然后决定下一步采取哪个行动，如果有的话。最后，代理决定使用哪些已采取的行动作为对主人的奖励；而主人会获得这个子集的总价值作为奖励。采取每个行动都会给代理带来一定的成本。因此，为了激励代理采取行动，主人预计会提供一个合适的契约。契约描述了主人向代理支付的金额作为主人通过代理的行动获得的奖励的函数。在本工作中，我们专注于研究线性契约，即主人将总奖励的一部分转移给代理的契约。我们假设主人的总奖励是基于一个形成给定 matroid 中独立集的行动子集计算的。我们建立了寻找最优线性契约（或计算相应主人效用）的问题与所谓的 matroid（不可靠性）问题之间的关系。一般来说，上述问题在添加元素的平行副本到给定 matroid 后被证明是等价的。
英文摘要：
In this work, we study sequential contracts under matroid constraints. In the sequential setting, an agent can take actions one by one. After each action, the agent observes the stochastic value of the action and then decides which action to take next, if any. At the end, the agent decides what subset of taken actions to use for the principal's reward; and the principal receives the total value of this subset as a reward. Taking each action induces a certain cost for the agent. Thus, to motivate the agent to take actions the principal is expected to offer an appropriate contract. A contract describes the payment from the principal to the agent as a function of the principal's reward obtained through the agent's actions. In this work, we concentrate on studying linear contracts, i.e.\ the contracts where the principal transfers a fraction of their total reward to the agent. We assume that the total principal's reward is calculated based on a subset of actions that forms an independent set in a given matroid. We establish a relationship between the problem of finding an optimal linear contract (or computing the corresponding principal's utility) and the so called matroid (un)reliability problem. Generally, the above problems turn out to be equivalent subject to adding parallel copies of elements to the given matroid.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
